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Manuscript Title: A finite-element toolbox for the stationary Gross-Pitaevskii equation with rotation
Authors: Guillaume Vergez, Ionut Danaila, Sylvain Auliac, Frédéric Hecht
Program title: GPFEM
Catalogue identifier: AFBD_v1_0
Distribution format: tar.gz
Journal reference: Comput. Phys. Commun. 209(2016)144
Programming language: FreeFem++ (free software, www.freefem.org).
Computer: PC, Mac, Super-computer.
Operating system: Windows, Mac OS, Linux.
Keywords: FreeFem++, Ipopt, Gross-Pitaevskii, Bose-Einstein, Finite element, Mesh adaptivity, Sobolev gradient.
Classification: 2.7, 4.9, 7.7.

Nature of problem:
The software computes 2D or 3D stationary solutions of the Gross-Pitaevskii equation with rotation. The main application is the computation of different types of vortex states (Abrikosov vortex lattice, giant vortex) in rotating Bose Einstein condensates. The software can be easily modified to take into account different related physical models.

Solution method:
The user has the choice between two robust and optimised numerical methods for the direct minimization of the Gross-Pitaevskii energy: a steepest descent method based on Sobolev gradients and a minimization algorithm based on the state-of-the-art optimization library Ipopt. For both methods, mesh adaptivity strategies are implemented to reduce the computational time and increase the local spatial accuracy when vortices are present.

Running time:
From minutes for 2D configurations to hours for 3D cases (on a personal laptop). Complex 3D cases (with hundreds of vortices) may require several days of computational time.